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till applet
If a spring with a mass
m
attached to it is slightly stretched or compresses with displacement
x
. The restoring force is given by
Hooke's Law
F
_{r}
(
x
)= 
k
x
,where
k
is a constant
The solution to this equation is a simple harmonic oscillation.
(negligible mass of the spring).
Consider a spring hanging freely, stretches a length dx when it made to support a load of mass m.
The force becomes
F
(
x
) = m
g

k
x
The
equilibrium position is x = m g /
k
Add
Damping force:
Suppose there is a viscous damping force
F
_{b}
= 
b
v
,
where
b
is a constant and
v
is the velocity of the load.
add external force that varies harmonically
F
_{ext}
= f
_{o}
sin( cwt )
w
^{2 }
=
w
_{o}
^{2 }

(b/2
m
)
^{2}
where
w
_{o}
^{2}
= k/m,
w
_{o }
is the nature frequency of the system
if c=0. then f
_{o}
= 0.
The net force acts on the mass is
F =
m
g 
k
x

b
v + f
_{o}
sin( cwt )
How to play?
You can enter values of
m, k, b, f
(
m
can also be changed with mouse click on
+/
button)
b=0., f=0.
simple harmonic motion(SHM)
b!=0. (try 0.1)
damped oscillation
f!=0. (try 5.0)
forced oscillation
You can drag the left mouse button to change the initial position of the mass.
Animation starts when the mouse button is released.
If you drag with right mouse button ( or press > Button),
the spring will also move with constant speed in the horizontal direction.
Green arrow : the displacement
x
measured from the unstretched point.
blue arrow : the displacement
x
measured from the equilibrium point (
F=0
).
red arrow : the velocity
v
of the mass.
Each time you click the mouse button, the coordinate of the mouse is shown in the text Field. (MKS unit,
x
/
v
verses
t
)
External driving force:
c=0. means there is no external force,
i.e.
f
_{o }
= 0.
otherwise F
_{ext }
= f
_{o }
* sin ( c*w* t), where w
^{2}
= k/m  (b/2m)
^{2}
till applet
©
FuKwun Hwang
Hans andra java applets
Översatt/anpassat SSVH
Jeff Forssell
Senaste uppdatering Tuesday, February 01, 2000
Fy/java/hwang/springWave/springWave.html